I wouldn't remove the cover on the auto pump. Tried this in my own Disco and diesel spilled out. I was told I was lucky the diesel seal held when I reassembled it.
Apparently you can remove the cover on the manual to bypass something there. Approach with caution is all I'd advise. Buzzing is normal.
I have the same problem, intermittently, quite a few threads on this, most go dead, but never a solution. I blame the green immobiliser unit at the side of the passenger footwell. If you can borrow a replacement with a matching keyfob it's worth a try. I'm certainly no expert on this.